Introductory Retrospective

The Era. Rapid Evolution of Science

Doraiswami Ramkrishna School of Chemical Engineering, Purdue University, West Lafayette, IN 47907

DOI 10.1002/aic.14191 Published online August 5, 2013 in Wiley Online Library (wileyonlinelibrary.com)

Neal Amundson (1916–2011) influenced the chemical engineering profession more profoundly than any other single individual, and in this article the author has attempted to capture the man and his era, as well as his lasting legacy. His influence extended well beyond those of other chemical engineers of renown, whether they were known for exploring and establishing new avenues, or for the resolution of outstanding issues, or for other forms of creative endeavors. Amundson reached into the depths of the profession, noted for its expanse, complexity and diversity that had led earlier efforts into a shrine of empiricism, to foster a culture of strongly scientific thinking with a mathematical edifice, which must be the crux of all engineering. The growth of chemical engineering science owes most significantly to Amundson’s extraordinary role as an educator, department head and leader, and to the lasting impact of his contributions to chemi- cal engineering research and practice. This article is in salutation of the man who came to be known as the Chief, and was responsible for an academic movement that raised the intellectual level of the chemical engineering pro- fession. VC 2013 American Institute of Chemical Engineers AIChE J, 59: 3147-3157, 2013 Keywords: amundson, chemical engineering science

Introduction The arrival of Neal Russell Amundson into the chemical engineering scene must be regarded as heralding his deliberate Olaf A. Hougen once challenged the author of this article effort to build the scientific base of chemical engineering. to produce an equation in a book out of which he had taught Mathematics was indeed to play a key role in this process but, chemical engineering in the 1920s. His challenge was of in his leadership role, it was a quest for the import of basic course prompted by the book’s scrupulous freedom from concepts of all science. This was not simply to be a paradigm equations! As an outgrowth of an engineering profession for shift, but a major cultural change. It deeply involved the crea- the production of chemicals, chemical engineering had its tion of model images of systems; penetrate them to their patho- beginnings in dissecting chemical processes into unit proc- logical limits with mathematical tools, and eliciting guidance esses and unit operations. Unit processes were concerned for experimentation in search of more complete understanding. with the nature of chemical transformations while unit opera- The department he built at Minnesota was a reflection of this tions focused on physical processes of separation, mixing, philosophy. It is the objective of this article to reflect on the and so on. The underlying methodology was largely empiri- Neal Amundson era and the evolution of chemical engineering cal with performance described by correlations linking inde- science during this period. In so doing, we will deliberate not pendent dimensionless groups of the system. The prevailing only on Amundson’s contributions and their impact, but also view of the early was that of a mechani- on his overall influence on the chemical engineering profession. cal engineer, who focused on the manufacture of chemicals. The introduction of material and energy balances by Lewis and Radasch1 andHougenandWatson,2 was a significant Educational Background and Early development in this growth phase of the chemical engineering Academic Days profession. It sowed the seeds of rationally thinking about sys- tems and analyzing them with conservation and thermody- Amundson obtained his Bachelor’s degree in chemical namic principles. It was a precursor to the more microscopic engineering from the in 1937, and view that followed with the institution of transport phenomena joined Standard Oil Co. (now ExxonMobil) in Baton Rouge by Bird et al.3 which laid the foundation for unifying the as a Process Control Engineer. Neal did not recall the expe- apparent diversity of unit operations and unit processes. rience as particularly interesting, because engineers were denied access to the company’s R&D facilities where the flu- idized catalytic cracker was in its early development. There Correspondence concerning this article should be addressed to D. Ramkrishna at were too many “nonproductive” activities that consumed his [email protected]. energy of which he had ”had enough” by the end of 2 years, VC 2013 American Institute of Chemical Engineers and he returned to the University of Minnesota for graduate

AIChE Journal September 2013 Vol. 59, No. 9 3147 studies. He enrolled for a Master’s degree in chemical engi- time was ripe for this activity to flourish. Also Neal had neering there. The Dept. of Chemical Engineering, at that noticed that chemical engineers were not familiar with matri- time housed in the chemistry building, was relatively young ces and introduced them in his courses. The application of but “competent” as Neal described it. He observed, however, matrices could not have had a better beginning than through that the research in the department was “mostly experimental the arrival of as a graduate student on the and dull.” Interestingly, Amundson received his Master’s scene, who subsequently grew to be one of the most distin- degree in chemical engineering in 1941 with the first ever guished academicians of chemical engineering. With Neal’s nonexperimental thesis! research contributions to be discussed later in this article, we There had been “very little mathematics” taught during his turn to other aspects of his academic career. undergraduate days at Minnesota so that Neal’s interest in Following Doc Mann’s unfortunate death in 1949, Neal mathematics was not aroused until after his bachelor’s degree. became the Acting Head of the department, while an exter- Curiously, while he was at Standard Oil, he and a few of his nal search was initiated by Dean Spilhaus for a new Head. colleagues attended evening classes at LSU on differential After some unsuccessful attempts, it was clear that someone equations taught by a Norman Rutt, whom Amundson fondly within the department should take over as Head. Edgar Piret, recalled as a very “charming fellow”! This seems to have a senior colleague of Neal was a potential candidate, but had sowed the seeds of his subsequent involvement with mathe- been rejected by the faculty. Any residual inkling that Dean matics. One wonders whether such excursions are at all a part Spilhaus may have had in offering the Headship to Piret, of students taking courses during graduate work today! was eradicated after his encounter with Neal on the issue. The years that followed were highly consequential for Thus, began the stellar academic career of Neal Amundson, Neal. In light of finding little mathematics in the Chemical a full Professor at age 35, and Head of the Dept. of Chemi- Engineering Dept., he switched to a PhD in mathematics cal Engineering at Minnesota in 1951. under the supervision of Hugh Turrittin at the University of Minnesota. A student of Rudolph Langer of Wisconsin, Tur- As Department Head rittin’s lineage stretched two generations back to the famous Amundson went about building his department with admi- American mathematician, G. D. Birkhoff. The final year of rable support from Dean Spilhaus, who discovered early that Neal’s doctoral thesis was spent at Brown University where Amundson thrived when he was otherwise left alone. his advisor was on sabbatical leave. This could well have Resources were scant at the University for building a strong been the defining period of Neal’s career, for he experienced research program. The focus had to be on hiring theoreti- at Brown an extraordinary atmosphere of mathematics that cians but perhaps also partially out of conviction that the he felt as if had “pulled him out of the water”! He returned profession needed theory at its stage of development. Chemi- to Minnesota in 1945 with a PhD in mathematics, euphoric cal engineering theoreticians were an undefined community about his experience at Brown in the company of eminent so that they had to be sought from other disciplines. Amund- mathematicians, and ideas that perhaps molded his own aca- son was not interested in hiring chemical engineers who pro- demic contributions the most. His doctoral dissertation bore fessed interest in conventional areas like heat and mass the title “Solution of a Nonlinear Partial Differential Equa- transfer. They had to be involved in arresting new directions tion of the Parabolic Type.” in depth. Bill Ranz, whom he hired with a PhD from the Neal began his academic career at the University of Min- University of Wisconsin, came as close to traditional ChE as nesota as an Assistant Professor of Mathematics. Even as a possible, but he certainly was an unusual thinker. His highly young, junior faculty member, his instinct for leadership had cited work on packed beds with Bob Marshall of Wisconsin begun to surface, for he had played an active role in chang- had won him the AIChE Colburn award in 1955. ing the face of Minnesota mathematics by initiating the The story of Amundson’s discovery of , move of an eminent mathematician by the name Stephen has often been told but bears repetition because it is an Warschawski from Brown University to head the Dept. of extraordinary one. While a Fulbright Scholar at Cambridge Mathematics at Minnesota. With Warschawski’s arrival, University in 1954/55, Amundson had the opportunity to many new courses were instituted, a full year of partial dif- visit ICI (Imperial Chemical Industries). There in their ferential equations to note in particular. research department he met young Rutherford Aris who had During this time, Dr. Charles Mann, then Head of the Dept. had no formal degree education. He had obtained an external of Chemical Engineering, would often approach Amundson Master’s degree from the University of which did suggesting that he move his department to help with teaching, not require him to attend the university. They went to lunch and educate students and faculty about how mathematics together and Aris asked Amundson about spending some could be applied to chemical engineering. After a few such time at Minnesota. Amundson had clearly been impressed in encounters that had appeared somewhat casual, Amundson the short time they had been together and agreed to have asked Mann to desist from such feelers if he was not going to him visit for a year which was to be spent collaborating on be serious about making him an offer! That indeed made the some articles. Before the work was completed, Aris had an difference and Amundson transferred to the chemical engi- offer from the . He promised to neering department as an Associate Professor in 1947. return the next summer to finish up the articles, which he Of his own admission, this move was most crucial to did. During the summer, however, he met his future wife Amundson’s career as a chemical engineering academic, and Claire. They returned to but Claire was keen to the leadership he came to exert on the profession. His inter- return to Minnesota and so Aris asked Amundson if he could est in chemical engineering had a surging revival at this come back. Amundson secured Aris an appointment as an stage. There was a crying need for the application of nonlin- Assistant Professor without a formal PhD degree with Dean ear mechanics to chemical reaction systems, and with the Spilhaus’ approval! Such a scenario was unimaginable even timely arrival of Olegh Bilous, an astute French student, the in those days anywhere else in the ! Aris had

3148 DOI 10.1002/aic Published on behalf of the AIChE September 2013 Vol. 59, No. 9 AIChE Journal about 12 publications then which obtained him an external Doctor of Science from the , U.K., but one with which he was not satisfied. Amundson suggested the topic of dynamic programming for a fresh dissertation that subsequently provided Aris with a regular PhD degree from the University of London. This culminated in the book entitled The Optimal Design of Chemical Reactors published by Academic Press, which has since become a classic.4 The foregoing story best captures the pioneer spirit with which Amundson built the faculty at Minnesota. Amundson had one simple strategy on hiring: “If I thought I was smar- ter than the fellow I was interviewing, I wouldn’t hire him!” That sums up his philosophy rather well. So there was an array of truly outstanding individuals that joined the Minne- Figure 1. Front row: Lanny Schmidt, Ken Keller, Neal sota faculty. Skip Scriven, who had obtained his BS in Amundson, Ted Davis, Gus Aris, Bob Carr, chemical engineering from the University of at Skip Scriven, Wei-Shou Hu; second row: Berkeley and PhD from the University of Delaware under Arnie Fredrickson, John Weaver, Alfonso the supervision of Bob Pigford, was a significant addition. Franciosi, Christie Geankopolis, Klavs Jen- He was an astounding theoretical fluid mechanician, who sen, Richard Oriani, Ed Cussler; third row: had then published a very fundamental article in Chemical Bill Smyrl, Bill Gerberich, Henry White, Mar- Engineering Science on the formulation of surface equations, tha Mecartney, Fennell Evans, David Shores, and had won the Colburn Award with his colleague in Shell Friedrich Srienc. Development, C. V. Sternling for their epochal contribution on Marangoni instability. sheets generally featured items that involved grueling prepa- Neal had a special eye for talent and saw it early. He rec- rations reaching into late hours of the night. It is amusing to ognized it in Arnie Fredrickson, who got his BS and MS recall occasional instances of one recitation instructor calling degrees in chemical engineering at Minnesota, and persuaded another (instead of the instructor-in-charge!) for answers to him to go to Wisconsin for his doctoral work. Arnie got his questions only to discover that neither was any closer to the PhD under Bob Bird’s supervision and returned to Minnesota solution! as an Assistant Professor. John Dahler arrived with a PhD in The underlying message in the foregoing account is that molecular theory from Joe Hirschfelder’s group at Wiscon- there was no way to emerge from the recitation experience sin. This had occurred in response to a plea from Neal to without a healthy understanding of chemical engineering! It Joe some years earlier for an exceptional student from the would be a stretch to expect that a surface scientist such as latter’s group. Shortly thereafter, Ted Davis joined the fac- Lanny Schmidt would teach a process control course any- ulty from the University of Chicago with a doctoral degree where else! This rigorous introduction to chemical engineer- in Theoretical Chemistry under the supervision of Stuart ing and interaction with ChE colleagues helped develop Rice. They were followed by Lanny Schmidt, a surface sci- strong collaborative research programs. The highly success- entist from the University of Chicago, Ken Keller, a chemi- ful Davis-Scriven collaboration in the areas of transport in cal engineer with a Biomedical engineering background from porous media and interfacial processes is an outstanding Johns Hopkins (who subsequently became President of the example (Figure 1). It is gratifying to know that even today University of Minnesota: 1985–1988), and Bob Carr, a Har- Minnesota continues to vigorously maintain this system vard Kineticist. Also worthy of note is the hiring of Henry under Frank Bates’ leadership. Tsuchiya, an experimental bacteriologist with whom Arnie The Minnesota faculty seemed much attuned to the system Fredrickson teamed up to start one of the earliest bioengin- just as the author was during his 1965/67 stay there as a eering programs in the country. temporary Assistant Professor. Amundson’s leadership has Neal’s grand idea was clearly to facilitate the import of had much to do with it, for it is not clear that such a system basic science into chemical engineering by hiring scientists would have been acceptable to faculty elsewhere. and then encouraging the cross fertilization of different The department’s reputation was surging in the early 1960s fields. He realized that this idea could succeed only if there and was attracting the best graduate students from the US was a way to introduce non-ChE’s to the field of chemical and abroad. Many talented postdocs and distinguished profes- engineering. This requirement was brilliantly met by a sys- sors came visiting the department from all over the world. tem of team teaching of undergraduate core courses, whose Gordon Beveridge (Scotland), Richard Mah (Singapore), success has been awe-inspiring! Bill Ranz is known to have Horst Brodowsky (Germany), Howard Brenner (Brooklyn) crafted this system, in which junior faculty began with being and Bill Schowalter (Princeton) are some examples. recitation instructors under the guidance of a course instruc- Following Amundson’s strategy for hiring faculty is unim- tor in charge of the main lectures. While the main lectures aginable in today’s circumstances, for he is reported to have had a sizeable number of students (well over 60 in the early kept close tabs on the impression left by the candidate on days), the recitation classes had about a score or more of stu- his faculty, as the interview was in progress, in order to be dents. Recitation instructors were required to attend the main able to make an offer often by the end of the day! lectures, thus, providing experience toward being instructors- Amundson rarely had faculty meetings. In Arnie Fredrick- in-charge at a later stage. The instructor in charge made up son’s words, “He led the department and ran it by consensus. recitation sheets that laid down the agenda for each class. He had ways to find out what each of his faculty members Especially when Skip or Arnie made them up, the recitation were thinking on issues and to inform them not only

AIChE Journal September 2013 Vol. 59, No. 9 Published on behalf of the AIChE DOI 10.1002/aic 3149 collectively but also individually of what he was thinking defined properties provided a perfect scenario for the applica- about the issues and if there was consensus on doing some- tion of linear programming. (The introduction of linear pro- thing we had a department meeting and took a voice vote gramming to chemical engineers had occurred in an article (ayes 12, nays none). If there was no consensus on a pro- by Fenech and Acrivos8). As a graduate student in 1960, the posed action there was no meeting and the thing was not author recalls, a special set of notes compiled by Amundson done. No doubt all of the things that he wanted the depart- on Linear Programming as part of his applied math course ment to do did not get done, but most of them did get done, sequence that all entering graduate students had to take. because everyone could see the rightness of what he wanted There is much to be said about this course sequence, which to do.” The faculty had little sense of the bureaucracy was the most popular in the Minnesota graduate program. that prevailed, probably, because Amundson protected them First, because of its focus on chemical engineering exam- from it. ples, it greatly motivated students. All too often, engineering The faculty met virtually every day at the Campus Club students have come away unable to see the relevance of for lunch where important departmental issues were fre- mathematics to engineering, when math instruction is left quently discussed. The chemical engineering table was entirely to mathematicians. well-known and often savored by colleagues from other Second, far from being a mindless prescription of algorith- departments usually chemistry or mathematics. Not surpris- mic procedures for solving equations, it dealt with theory in ingly, the department had an unusual measure of collegiality! sufficient pith to create notable returns from its use. For This was academic leadership at its best! One must concede, example, Acrivos and Amundson9 showed how the use of however, that Amundson’s methods could have had unaccept- matrix theory could lead to calculation of downstream com- able consequences if they were in the wrong hands. Indeed positions in a multicomponent rectification column without academia has evolved to ensure against such odds, but, sadly involving any of the intermediate plate compositions. Using insulated from the boons of such inspired leadership! a similar approach to the stripping section, a mass balance at George Stephanopoulos was Amundson’s last hire which the feed plate becomes feasible simply from specification of Neal is reported to have celebrated with “having hired Jesus the tops and bottoms product of a distillation column of arbi- Christ”, a quip that would have been clear to anyone then trary height! Such insight will not accrue from routine use of familiar with the looks of George! Indeed this was a signifi- algorithms. cant hire that led to an outstanding academic family of Third, the course delved into mathematical concepts and researchers in Process Systems Engineering. promoted mathematical thinking, thus, arousing the curiosity Neal was a colorful personality with a great sense of of engineering students to take more advanced courses in humor; for a particularly entertaining account of this, the mathematics. Amundson’s book on Mathematical Methods in reader is referred to an unpublished article by Arnie Fre- Chemical Engineering; Matrices and their Application, was drickson who can be contacted for a copy of the same by published by Prentice Hall in 1966.10 email at [email protected]. An article by Acrivos and Luss Amundson maintained close contact with the Mathematics for the National Academy of Sciences provides another 5 department at Minnesota. At one time he even had to take the exciting account of Neal Amundson’s life. mantle of Headship of the math department for an interim period. Chemical engineering students were encouraged to As An Academic Researcher and Leader take high-level courses in . James Serrin, Although Amundson’s main research area was, what came Hans Weinberger, Don Aronson, Larry Markus, George Sell, to be known as, Chemical Reaction Engineering, many of Willard Miller and many others of the Dept. of Mathematics his earlier articles were designed to show the utility of math- were close allies of Amundson and Aris. Graduate students ematical tools that had not been adequately explored in the enjoyed this atmosphere with many developing new applica- past. Broadly, he was driven by a desire to squeeze every bit tions of mathematical methods. It was definitely a period of of understanding out of a system, by imposing all the mathe- change in which chemical engineers raised questions about matical tools at his disposal on its model. Deeply ad-mixed how to think quantitatively about systems. Neal’s belief in with this was a curiosity for interesting pathologies that fre- communication with mathematicians was infectious. The quently led him to quip: “I like to work on interesting prob- author, in particular, was greatly influenced by this. To effi- lems!” The essence of this remark could be understood only ciently communicate with mathematicians called for being by one who had experienced the discovery of an unexpected mathematically literate, which involves some territorial trans- system behavior and the unusual insight that derives from it! gression into mathematics. Neal used to refer to a need for Neal seized the ripe opportunity for mathematical analysis familiarity with “poor man’s functional analysis” that led us to of adsorption columns toward application to chromatography. collaborate for several years on a book published by Prentice In light of the application of chromatography to a diverse vari- Hall in 1985,11 that exposed chemical engineers to linear oper- ety of separation processes, the Lapidus-Amundson articles ator methods in solving problems with chemical reaction and continue to be highly cited; the one published in 19526 has transport. This collaborative effort, often at our homes (Figure currently 723 citations. Relating the nonlinearity of adsorption 2), had numerous scholarly discussions interspersed with equilibria to the appearance of shocks and discontinuous solu- scotch and lively conversation during happy hour that pre- tions of hyperbolic systems, required serious exposition. Thus, sented a picture of Neal in a domestic environment. Neal had the three volumes of First Order Partial Differential Equa- an earthy integrity about him, and a sense of modesty that tions, published by PrenticeHall,7 with Hyun-Ku Rhee and matched his intolerance for nonsense. The author often has Rutherford Aris, followed in subsequent years. nostalgic reminiscences of his wife Shirley’s extraordinary Chemical engineering, with numerous stage-wise opera- hospitality during these visits. tions, created a natural need for familiarity with linear alge- Neal was among the first in ChE to introduce the use of bra. Blending of petroleum stocks for specific products with computers, which started with Univac 1103, followed by

3150 DOI 10.1002/aic Published on behalf of the AIChE September 2013 Vol. 59, No. 9 AIChE Journal ear effects until the articles of Schmitz (a distinguished former student of Amundson) and coworkers16 laid it to rest by vivid, experimental demonstration of steady-state multiplic- ity, hysteresis and other aspects of nonlinear behavior. The author also recalls a successful consulting experience17 with Conoco-Phillips in which a continuous Fischer-Tropsch reac- tor switched, under the same conditions, from a steady state with liquid hydrocarbon product to one with a gaseous prod- uct, containing largely methane, apparently due to some “unknown” perturbation! Nonlinear analysis of chemical reac- tors has since grown in powerful ways with the use of bifur- cation theory (Uppal et al18,19, Balakotaiah and Luss20). While computation was the hallmark of much of the fore- going work, the mathematician in Amundson sought to find ways in which a priori analytical criteria for steady-state Figure 2. The author and Neal Amundson discussing multiplicity could be derived, using mathematical analysis applied mathematics at Ramkrishna’s home. without involving much computation. He published some of 21 [Color figure can be viewed in the online issue, which is these articles by himself, numerous others with Dan 22 23 available at wileyonlinelibrary.com.] Luss , and with . The growth of mathemat- ics in the chemical engineering profession, which must be viewed as largely due to the Amundson-Aris School, is Control Data 1604. The graduate students in the department 24 were well into regularly using them on their thesis projects. traced in an article by Ramkrishna and Amundson. The analog computer had special attraction in the 1950s and Neal constantly strove for insights that could simplify mathematical models. An early example is that of polymer- 60s because they were easy to patch up for examining solu- 25 tion trends quickly with variation of system parameters. It is ization in which Zeman and Amundson sought to convert a believed that the first analog plot was published in ChE by discrete polymer distribution, described by a large number of Acrivos and Amundson,12 who investigated the solution of ordinary differential equations, into a continuous distribution transient stage-wise operations. This influenced similar plots of polymers satisfying a single-partial differential equation. 13 This concept spread to other areas such as the analysis of by other students (e.g., Ramkrishna et al. who analyzed bio- 26 reactors). Liu and Amundson14 solved on a digital computer reaction mixtures (Gavalas and Aris ) and to distillation models.4 He was also the earliest, along with Valentas and approximately 200 simultaneous ordinary differential equa- 27 tions for a polymerization system. Indeed the use of a com- Bilous, to model dispersed phase systems using population puter emerged as a natural complement to the formulation of balances. mathematical models that resulted from the perspective that As the first American editor of Chemical Engineering Sci- Amundson generated. Hence, these foregoing firsts must be ence from 1956 to 1972, Amundson actively promoted viewed as having heralded the computational approach to articles that dealt with theory. (For a time, Danckwerts, the chemical engineering problems in the years to come. editor from had felt an overdose of mathematics in Neal Amundson, along with Rutherford Aris (Figure 3), the journal although he was himself a trailblazer in its use!). arguably founded the subject of chemical reaction engineering Chemical Engineering Science grew to be a premier chemi- with its full complement of reactor dynamics, optimization cal engineering journal with several outstanding publications and control. The articles by Bilous and Amundson,5 and Aris in those formative years. Subsequent American editors, and Amundson,15 raised the issue of steady-state multiplicity Arnie Fredrickson, Rutherford Aris, Matt Tirrell, and Bob with the mathematical arsenal of Liapunov stability, which Brown all had Minnesota roots of one kind or another. This spurred a splurge of articles on the subject. Despite this, skep- is also true of the AIChE Journal which has had editors Mor- ticism raged among practitioners on the reality of such nonlin- ton Denn, Matt Tirrell, Stan Sandler, the present editor Mike Harold and Associate Editor, George Stephanopoulos with similar roots. Amundson’s accolades grew steadily over the years both in the US and abroad. Not surprisingly, he won the top AIChE honors, was elected to the US National Academies of Engineering, Science and of Arts and Sciences, and bestowed with Honorary doctorate degrees from many uni- versities. After 25 years of his Headship at Minnesota, Amundson perhaps felt the urge to make way for new lead- ership. He may have sensed a completion to his mission, but cultural changes in the university may also have added to his desire to step down. May be it was an opportune time for relocation to warmer weather!

The Years Figure 3. Neal Amundson and Rutherford Aris. Amundson’s move to the University of Houston in 1977 [Color figure can be viewed in the online issue, which is was spearheaded by Dan Luss, one of his highly distin- available at wileyonlinelibrary.com.] guished students, who headed the Dept. of Chemical

AIChE Journal September 2013 Vol. 59, No. 9 Published on behalf of the AIChE DOI 10.1002/aic 3151 Tom Edgar and others who distinguished themselves in unique ways. Andreas Acrivos, another of Amundson’s early graduate students (PhD, 1954) is one of the most distinguished acade- micians in chemical engineering. After a doctoral disserta- tion on the use of matrix theory in distillation, he established his own School of fluid mechanics that has led to a rich gen- ealogy replete with a flourishing family of outstanding aca- demics with a first generation comprising Gary Leal, Bill Russell, John Brady, and many others. A stream of exceptional academics from Amundson fol- lowed of whom, Dale Rudd, Roger Schmitz, Hyun-Ku Rhee, Dan Luss, Arvind Varma and Sankaran Sundaresan are but a sample! Omission of mention of many other academics of high quality is indeed regrettable. A somewhat more detailed Figure 4. Amundson at one of his birthday parties at yet very incomplete account of the many outstanding aca- Houston with Andy Acrivos, Gus Aris, Dan demic graduates can be had from a publication of his col- Luss, Skip Scriven. lected works.31 Many of Amundson’s students subsequently rose to be Engineering there. Clearly, Dan had inherited not only Department Heads, Deans, Provosts or Presidents, of which Neal’s creative instincts in research but also some of the lat- Lapidus, Acrivos, Schmitz, Luss, Varma, Rhee, Zygourakis ter’s astuteness for leadership (Figure 4). His maneuver of represent outstanding examples. Numerous others joined Neal’s move to the University of Houston was a masterly industry to become corporate leaders. Perhaps the most dis- accomplishment that soon sent the ranking of his department tinguished of them is Lee Raymond who rose to be the Pres- soaring to a spot in the top 10 in the country! ident of ExxonMobil (Figure 5). Ron Zeman (Dow Corning), At Houston, Amundson continued his activity in reaction Ken Valentas (General Mills, Pillsbury), and Dick Schmeal engineering with fervor, graduating many outstanding stu- (Shell Development) and many more rose to high positions dents. Deserving special mention are Sankaran Sundaresan, in their respective organizations. Stratis Sotirchos and Srinivas Bette. For a while, he was Amundson’s strategy was to allow graduate students con- absorbed in many fundamental issues with the Stefan Max- siderable freedom for developing their work. He did not well equations for multicomponent mass transfer that seemed breathe down their necks, but the author does recall some of to have not received prior attention. He held a joint appoint- Amundson’s students feeling stretched further just when they ment with the mathematics department at Houston, which had the image of being done with their theses! led him to teach an undergraduate calculus course for a while. In 1987, he became the Dean of Faculty and served in that capacity for 2 years. In course of time, his involve- ment with the Dept. of Mathematics grew progressively with collaborating colleagues there. He published numerous articles with a young junior colleague, Jiwan He for whom he had often expressed special appreciation. It is the author’s view that Neal was moving more toward computation than analysis during this period of time. Yet he retained a special place in his heart for creative analysts like Marty Feinberg, now at Ohio State University. Neal collaborated for several years with John Seinfeld of Caltech on atmospheric modeling publishing several land- mark articles28–30 on thermodynamic phase equilibria in aero- sol systems. John is a distinguished member of Amundson’s academic tree as a former student of , one of Amundson’s early graduate students.

Academic Descendants Amundson’s inspiring guidance of graduate students pro- duced many outstanding leaders in academia and industry. Lapidus joined the chemical engineering department at Princeton and pioneered the computational area of chemical engineering, publishing numerous articles on process synthe- sis and control. He soon rose to be the department head but his life ended prematurely at the age of 52. In the short span of his life, he had published numerous books on applied Figure 5. Neal Amundson with former student Lee Ray- mathematics and risen to stardom by winning several mond former CEO of ExxonMobil. awards. Lapidus’ academic tree got off to an impressive start [Color figure can be viewed in the online issue, which is with a spurt of outstanding academics such as John Seinfeld, available at wileyonlinelibrary.com.]

3152 DOI 10.1002/aic Published on behalf of the AIChE September 2013 Vol. 59, No. 9 AIChE Journal Amundson’s Impact on Chemical Engineering micellar solutions and transitions, behavior of fluid interfaces, Amundson’s impact on the chemical engineering profes- flow and transport through porous media, and so on. Ted’s sion must be measured not just from his own research contri- energy knew no bounds as, in the midst of all his activity, he butions or from those of the impressive array of leaders on served 12 years as Department Head and 10 years as Dean. his academic tree. The influence that his presence has had It should be evident that what was viewed as a gamble by on the evolution of chemical engineering science in general some, when Amundson sought to overhaul chemical engi- profoundly contributes to his impact. In this regard, it is of neering culture, has clearly led to a profession rich in its sci- interest to do some retrospective evaluation of Amundson’s entific content, able to contribute in many more ways to adventurous pursuit of hiring scientists that invoked criticism societal issues than ever before. This is an extraordinary from conservative sources. Our focus below is on how the accomplishment by an individual with so many different fac- scientists that Amundson hired collaborated with chemical ets that, to evaluate Amundson’s accomplishments, the pun- engineers in the faculty to establish new directions and pro- dits must discard the metrics that academics have come to duce new leaders in their respective fields. love these days and find something quite different! The impact that Aris has had on the use of mathematics in Finally, it will be interesting to reflect on the many ways reaction engineering, and chemical engineering in general has in which Amundson has contributed to the engineer’s no parallel. Aris’ academic tree has an imposing collection of thought process in quantitative understanding of things in high-powered academics such as Morton Denn, George Gava- engineering and science. In this regard, the field of biologi- las, Harmon Ray and many more. Furthermore, the collabora- cal sciences, a significant area of current chemical engineer- tion of Lanny Schmidt with Gus Aris also produced ing research, seemed ideally suited for discussion. Although outstanding chemical engineers like Yannis Kevrekedis, Dion Amundson had actively organized the development of bio- Vlachos and several others. Besides being responsible for the logical research at Minnesota from as early as the 1950s, his growth of surface science, Lanny established himself a pre- own activity had not encompassed even in a minor way any mier reputation as a chemical reaction engineer. Of Ruther- issues of biological interest. Yet many developments in bio- ford Aris, an intellectual giant in his own right, not enough logical modeling have gained from his insight on chemical could ever be said that will do justice either to his rare schol- reaction systems. Toward establishing this, we will focus on arship or to his exemplary collegiality! the very important area of mathematically modeling living Amundson’s hiring of Henry Tsuchiya, a bacteriologist, in cells. It derives its importance from the diversity with which the late fifties must be regarded as an exceptional stroke of cellular activity impacts society through implications to envi- insight. Henry teamed up with Arnie Fredrickson to produce a ronment, energy and health, and to products of varied inter- long pioneering program of Biological Engineering with which ests such as food, cosmetics, pharmaceuticals and drugs. the author had the distinct pleasure of being associated early. Modeling cells has been of interest to researchers of Fredrickson, Tsuchiya and Aris produced many of today’s diverse backgrounds, biophysicists, biochemists, biologists, leaders in Bioengineering such as Greg Stephanopoulos, Mike computer scientists, and engineers of almost all kinds. Con- Shuler and others. Doug Lauffenburger, another outstanding sequently, there have been different approaches, ranging bioengineering leader in the same light, came from Ken Kel- from ultrasimplified models to very complex models that do ler’s group. virtually everything occurring in the cell. Naturally, there are Ted Davis’ rise to stardom was phenomenal. His collabora- different goals associated with such varied models. Thus, an tive activity was exceptional over the years as it included not ultrasimplified model (of which the Monod model is an only Skip Scriven but also many others on the faculty both old example) can only be expected to describe some gross fea- and new (Figure 6). The Davis-Scriven collaboration that tures such as how much biomass can be produced from a lasted many years produced outstanding academics such as certain amount of carbon substrate in a batch reactor, or for Ron Larson, Eric Kaler (the current President of the University estimating the dilution rate in a continuous reactor to prevent of Minnesota), and many others. This group of students made washout, and so on. An example of the most complex model pioneering contributions to the understanding of nanoparticles, may be found in a recent article by Karr et al.32 Evaluation of different models would of course require rational consid- eration of the returns on investment, which can be fairly sophisticated. However, for our present purposes, we will examine how compromises can be made on complexity through ideas that have often moved Amundson to find sim- pler descriptions of systems. Metabolism involves a very large number of chemical reactions involving external nutrients, and thousands of intra and extracellular metabolites. The cell is an (expanding) open system with transport of nutrients into it and products transported out. The steady state description involves a very large number of homogeneous algebraic equations with many more unknowns than equations. Cellular metabolism is, thus, to be described by a large number of reaction rates contained in a metabolic flux vector of stupendous dimen- Figure 6. Matt Tirrell, Rutherford Aris, Ken Keller, Neal sion. Targeting the calculation of intracellular reaction rates Amundson, and Ted Davis. based on measurements of relatively accessible exchange [Color figure can be viewed in the online issue, which is rates with the environment is tantamount to wrestling with a available at wileyonlinelibrary.com.] set of equations far outnumbered by the number of

AIChE Journal September 2013 Vol. 59, No. 9 Published on behalf of the AIChE DOI 10.1002/aic 3153 Palsson’s original strategy is one of seeking the edge of a “flux cone” that contains all feasible solutions of the steady- state problem along which the rate of biomass synthesis is maximized. The corresponding scenario in “yield space” is represented by a convex hull with one (or more) of its verti- ces purporting to be the solution. It is possible to view each vertex as a pathway option of the organism so that the pref- erence for one that maximizes biomass yield may be viewed as a consequence of metabolic regulation. A singular aspect of metabolism is the presence of regula- tory processes, which selectively control syntheses and activ- ities of enzymes that catalyze the numerous cellular reactions. The complexity and diversity of this regulation Figure 7. Convex solution space of a metabolic sys- leave much understanding to be had toward a suitably tem. dynamic description of this reaction system such as Amund- [Color figure can be viewed in the online issue, which is son would have preferred. However, dynamic models of available at wileyonlinelibrary.com.] metabolism have graced the literature in varying degrees to which regulation has been included or ignored. A dynamic unknowns. Of early concern to Amundson4 was the solution approach to account for regulatory processes in a compre- of linear algebraic equations precisely under the circumstan- hensive way lies in the author’s cybernetic idea36 that attrib- ces just outlined earlier? The strategy in biochemical systems utes regulation to a survival effort of the organism by theory33 of using least squares to estimate either fluxes (or optimally investing its constrained resources toward prefer- rate constants in a dynamic framework) is a consequence of ential synthesis of enzymes in conjunction with judicious defining the generalized inverse of nonsquare matrices. control of their activities. This approach implicates in metab- A very astute approach to metabolic modeling due to Pals- olism many other pathway options with potentially sizeable son and coworkers34,35 is the postulate that cellular metabo- contributions to the organism’s survival goal. The required lism is guided by the objective of maximizing the yield of mathematical framework was that of optimal cell mass. The formulation does away with many possible espoused by Rutherford Aris37 and Neal Amundson38 for pathway options out of a large network and, with a mere sin- numerous other chemical engineering applications. gle measurement of the rate of substrate uptake from the When viewed in the flux cone, the dynamic approach environment, positions itself to predict the entire metabolic envisages many other edges of the cone that could contribute flux vector (Figure 7). This exceptional leverage of a meager to metabolic transients. In yield space, the metabolic state measurement is enabled by the power of linear programming becomes a convex combination of many vertices and so in awesome confluence with the stoichiometric edifice that is could move within the interior of the convex hull as, for the hallmark of all chemical reactions. This is the very sce- example, the reactor trajectory in the phase plane plots of nario in the petrochemical setting, which offered several Bilous and Amundson.5 Dynamic optimization in the cyber- alternative paths to manufacturing a product that led Amund- netic approach leads to a temporally varying convex combi- son to introduce linear programming several years earlier in nation of vertices of the convex hull. a graduate course. Students became familiar with the alge- The chemostat or a steady state well-stirred continuous braic formulation of chemical reactions in terms of intrinsic biological reactor fed with a constant concentration of reaction rates. Exposure to linear programming further led to nutrients with simultaneous withdrawal of the culture has familiarity with convex sets, convex analysis, and the sim- been a great tool in the study of metabolic phenomena. plex strategy of switching from one extreme point to another Although numerous publications exist in the application of in quest of the optima of linear functionals, and so on. These nonlinear analysis to bioreactors featuring mostly extracellu- have come to be essential concepts of metabolic analysis! lar variables, studies of the phenomenon of steady-state mul- tiplicity and investigation of pathological transient behavior have been few in regard to studying metabolism. Conse- quently, many potential profoundly variable aspects of meta- bolic behavior remain obscurely buried. For example, bacteria pregrown on glucose, when presented with a mix- ture of glucose and pyruvate, tend to preferentially consume glucose. However, on prior growth with pyruvate, the bacte- ria use both pyruvate and glucose right from the beginning. This aspect of regulatory behavior has strange consequences to steady states in a chemostat. Figure 7 shows the steady- state behavior of fermentation product formate in a bacterial chemostat fed with a mixture of glucose and pyruvate.39 The multiple hysteresis behavior shown in the figure is of course reminiscent of the many articles published by Amundson, Figure 8. Multiple steady states in a continuous biolog- Aris and numerous other reaction engineers. ical reactor. While the foregoing steady state multiplicity is a manifes- [Color figure can be viewed in the online issue, which is tation of nonlinearity, two interesting issues that stand out available at wileyonlinelibrary.com.] are (1) the source of nonlinearity is associated primarily with

3154 DOI 10.1002/aic Published on behalf of the AIChE September 2013 Vol. 59, No. 9 AIChE Journal the optimal choice behavior, and (2) the metabolism may involve not only quantitative differences in specific intracel- lular reactions but also in the choice of reactions for metabo- lism. This introduces an element of mechanistic causality in metabolic behavior well beyond the statistical causality that bioinformaticists currently seek from high-throughput data. In other words, an explanation may be available of variabili- ty of metabolic behavior by relating to the cybernetic sur- vival goal of the organism. An area of profound practical significance initiated by Bai- ley40 is the area of metabolic engineering in which genetic var- iations are introduced into a microorganism toward increasing the productivity of some metabolite of interest to a specific application. (Bailey had begun his academic career at the Uni- versity of Houston in dynamic systems theory and was indeed influenced by Amundson). The nature of network changes that would accomplish the desired increase in productivity becomes a crucial associated question. More precisely, the identity of gene “knock-in” and/or “knock-out” strategies would depend on the sensitivity of the governing flux to such changes. The problem of determining sensitivity of reacting systems to vari- ous operating parameters was first introduced by Amundson5 although it was in connection with behavior. The pertinence of this methodology (subsequently further devel- Figure 9. The Amundson Report 41 oped by Varma and Morbidelli ) to metabolic engineering is [Color figure can be viewed in the online issue, which is further accentuated by the role of “metabolic burden” in assess- available at wileyonlinelibrary.com.] ing the capabilities of an engineered organism. Amundson’s concern for simplified perspectives of com- Chair of a Committee charged with finding the research plex systems has general import. The characterization, as needs and opportunities for chemical engineering. The com- pointed out earlier, of polymeric reaction systems, in which mittee’s task was to identify new high-impact areas, and to a single-partial differential equation in polymer length, find leading experts in them who could define new directions viewed as a continuous variable, replaces a large number of for research. Neal picked James Wei, then at MIT, as the differential equation for polymers of discrete lengths. A dis- Vice Chair, and a number of other leading chemical engi- cretized approach to solving such a partial differential equa- neers in the US. In 1988, the NRC committee submitted its tion could entail a scale of polymer length considerably report, entitled “Frontiers in Chemical Engineering,” that set coarser than purely integral values, thus, effectively implying new directions to the profession (see Figures 9 and 10). a form of “lumping” polymeric species.19 Lumping reaction systems has been of interest to numer- ous other researchers. In particular reference to metabolic systems, the concept of lumping fluxes of pathway options offers prospects of containing pathway diversity. While the flux balance approach of Palsson and coworkers has been amenable to genome scale metabolic networks, dynamic models for the same must grapple with their identification because of an overabundance of parameters. In this connec- tion, the concept of lumping has considerably enhanced the prospects of applying cybernetic models by drastic reduction in the number of parameters for identification.42 It has been the author’s objective in this section to show how Amundson’s disposition to mathematical modeling and basic thinking has had notable impact even on an area that was not part of his activity. Relating developments in meta- bolic modeling to Amundson’s endeavors has consequently come about by the abstract implications of the latter. This is as it must be, for the power of mathematics lies in its unify- ing abstraction, notwithstanding the viewpoint of some that abstraction is a deterrent to realistic thinking.

Frontiers in Chemical Engineering: The Amundson Report Although this section must be regarded as part of Amund- son’s impact, it deserves to be treated separately. In 1986, the National Research Council appointed Neal Amundson as Figure 10. On the Amundson Report

AIChE Journal September 2013 Vol. 59, No. 9 Published on behalf of the AIChE DOI 10.1002/aic 3155 Significant aspects of this change are its closer association on the frontier areas has unfortunately created serious neglect with the sciences, the very direction in which Amundson had of the core areas of chemical engineering.46 Faculty are anx- sought to develop chemical engineering at Minnesota and a ious for their students to get started on research with minimal shift toward product engineering from its almost exclusive course work. Consequently, most departments have students past involvement with process engineering. The report select their advisors well before their first semester is over in stressed focusing on identified new frontier areas, but with a contrast with the earlier practice of almost a year. This is per- simultaneous need to preserve core competence. That these haps uncorrectable in current circumstances. Some depart- changes have taken root is clearly evident from the current ments have labored to provide support for graduate students orientation of most chemical engineering departments in the during their first semester or year through endowments. How- United States. ever, the pressure to get an early start on research is not alle- An article by Carranza43 reflects on the Amundson report viated. The result is graduate students entering frontier areas with reactions from various sources. Particularly noteworthy with a much weaker background of core concepts that is the strong criticism by Astarita44 who foresaw a weaken- brought ChEs to these fields in the first place! Perhaps this ing of core strength in chemical engineering. This perception issue is more applicable to some areas than others. However, obviously arose out of concern that exclusive funding of it is definitely a matter of concern that core strength has suf- frontier fields would result in progressive neglect of the core fered depletion and would continue in this trend without a areas. Perhaps there will be agreement among most academi- concerted effort to reverse it. In this regard, chemical engi- cians that this is already occurring. The funding focus on neering departments must strive to retain a strong program of interdisciplinary research has virtually eliminated the single core chemical engineering courses, viz., Transport Phenom- investigator! Amundson was himself a victim of this phe- ena, Chemical Reaction Engineering, Thermodynamics and nomenon that led him to disacknowledge any “alphabetical Applied Mathematics and Systems Engineering. A further agency” that provided him support beside the University of complicating issue in this regard is that entering students Houston.45 True to the call for interdisciplinary research by seem less prepared with core background from their under- the Amundson report, he did of course participate in interdis- graduate studies. In particular, students seem less prepared ciplinary research in atmospheric modeling with substantial with mathematical concepts than before. There is a higher federal and state funding. demand for computation in math courses, by faculty col- leagues, than for analysis. Often students can solve linear Concluding Remarks and Perspectives algebraic equations, using standard software, with no clue about the necessary and sufficient conditions for the existence Amundson influenced the course of evolution of the entire of solutions! Granted that available software such as MAT- profession of chemical engineering in multifarious ways. He LAB and MATHEMATICA are amazing in their capabilities recognized the need for replacing empiricism by enforcing a and it would be wasteful to labor through calculations, by not stronger scientific base and orienting chemical engineers to using them, but the question arises. Should students be using think quantitatively. This he accomplished through (1) his such software, for instance, before learning elementary con- own research in chemical reaction engineering, (2) his lead- cepts of vector algebra or to solve linear differential equa- ership as department head by recruiting faculty from the sci- tions? A strong applied math course should focus on ences, providing for their training in chemical engineering concepts, while use of software could be encouraged in appli- fundamentals through a unique process of undergraduate cation oriented courses. teaching, (3) his encouragement of collaborative programs of In order for core areas to grow, interdisciplinary projects scientists with chemical engineers in the faculty generating must play greater emphasis on participation of core faculty. leaders in new areas, (4) his editorship of the journal Chemi- Although not a sizeable fraction, from the author’s experi- cal Engineering Science, and (5) his national leadership ence, there still exist entering graduate students with a strong under the auspices of the National Research Council, which professed interest in core areas. What opportunities can such helped to define new directions in a changing world, thus, students have for academic development with a bright expanding greatly the potential of chemical engineers to con- future? If they wanted to pursue an academic career, could tribute to the solution of societal problems. Most impressive they successfully compete with other academic aspirants in examples of this are in academics such as Bob Langer of the frontier areas? While faculty must wrestle with these MIT, and Nicholas Peppas at UT-Austin. Nicholas, in partic- issues on their own to some extent, academia on the whole ular, has been vocal in his acknowledgment of the Amund- should be concerned about it so that the strong core back- son School even without a formal connection to it! ground that has made chemical engineering such a vibrant Indeed, in the years following the Amundson report, the profession will continue to thrive. These questions would modus operandi of engineering research has evolved to per- very much be in accord with Amundson’s concerns! forming in groups with complementary expertise, but with a healthy understanding by each of what each research partner brings to the table. This has been a wholesome attribute of Acknowledgments engineering research, as it is able to address larger problems The author gratefully acknowledges feedback from Andy with higher impact and relevance to society. While some Acrivos (who corrected some factual errors), Arnie Fredrick- argue that the multidisciplinary investigatory approach has son, George Stephanopoulos and Mike Harold. George’s marginalized the contribution of the single investigator the uninhibited criticism helped produce a manuscript that has contribution of chemical engineers to a multitude of far- no resemblance to its early version. ranging problems is undeniable. 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AIChE Journal September 2013 Vol. 59, No. 9 Published on behalf of the AIChE DOI 10.1002/aic 3157